Answer:
The new vertices are: [tex](-2,3),(-4,3),(-2,7),(-4,7)[/tex]
Step-by-step explanation:
The given vertices are [tex](3,-2),(3,-4),(7,-2),(7,-4)[/tex]
Rule for reflection about x axis is [tex](x,y)[/tex]→[tex](x,-y)[/tex].
So, [tex](3,-2)[/tex]→[tex](3,2)[/tex]
[tex](3,-4)[/tex]→[tex](3,4)[/tex]
[tex](7,-2)[/tex]→[tex](7,2)[/tex]
[tex](7,-4)[/tex]→[tex](7,4)[/tex]
Now, new vertices after reflection about x axis are [tex](3,2),(3,4),(7,2),(7,4)[/tex].
Rule for 90 degree rotation counter-clockwise is [tex](x,y)[/tex]→[tex](-y,x)[/tex].
So, [tex](3,2)[/tex]→[tex](-2,3)[/tex]
[tex](3,4)[/tex]→[tex](-4,3)[/tex]
[tex](7,2)[/tex]→[tex](-2,7)[/tex]
[tex](7,4)[/tex]→[tex](-4,7)[/tex]
Therefore, the new rectangle after reflection about x axis and rotated 90 degrees counter-clockwise has the following vertices:
[tex](-2,3),(-4,3),(-2,7),(-4,7)[/tex]
